Problem: Solve for $n$, $ \dfrac{4n - 3}{5n - 4} = \dfrac{1}{10} $
Multiply both sides of the equation by $5n - 4$ $ 4n - 3 = \dfrac{5n - 4}{10} $ Multiply both sides of the equation by $10$ $ 10(4n - 3) = 5n - 4 $ $40n - 30 = 5n - 4$ $35n - 30 = -4$ $35n = 26$ $n = \dfrac{26}{35}$